Question

If f(x) = log3 (x + 1), what is f−1(2)

Answer 1

Firstly, we'll find y = f⁻¹(x):


`f(x)=\log_3(x+1)\\\\ x=\log_3(y+1)\\\\ y+1=3^x\\\\ y=3^x-1\\\\ f^(-1)(x)=3^x-1`

So:


`f^(-1)(x)=3^x-1\\\\ f^(-1)(2)=3^2-1\\\\ f^(-1)(2)=9-1\\\\ \boxed{f^(-1)(2)=8}`

Answer 2

Answer: The value is 8.

Step-by-step explanation: Given function is

`f(x)=\log_3(x+1).`

we are given to find the value of
`f^(-1)(2).`

Let us consider that

`f(x)=y~~~~~\Rightarrow x=f^(-1)(y).`

So, we have

`f(x)=\log_3(x+1)\\\\\Rightarrow y=\log_3(f^(-1)(y)+1)\\\\\Rightarrow 3^y=f^(-1)(y)+1\\\\\Rightarrow f^(-1)(y)=3^y-1.`

If y = 2, then we have

`f^(-1)(2)=3^2-1=9-1=8.`

Thus, the required value is 8.